Results are presented from the first underground data run of ZEPLIN-II, a 31 kg two-phase xenon detector developed to observe nuclear recoils from hypothetical weakly interacting massive dark matter particles. Discrimination between nuclear recoils and background electron recoils is afforded by recording both the scintillation and ionisation signals generated within the liquid xenon, with the ratio of these signals being different for the two classes of event. This ratio is calibrated for different incident species using an AmBe neutron source and 60Co [gamma]-ray sources. From our first 31 live days of running ZEPLIN-II, the total exposure following the application of fiducial and stability cuts was 225 kg × days. A background population of radon progeny events was observed in this run, arising from radon emission in the gas purification getters, due to radon daughter ion decays on the surfaces of the walls of the chamber. An acceptance window, defined by the neutron calibration data, of 50% nuclear recoil acceptance between 5 keVee and 20 keVee, had an observed count of 29 events, with a summed expectation of 28.6 ± 4.3 [gamma]-ray and radon progeny induced background events. These figures provide a 90% c.l. upper limit to the number of nuclear recoils of 10.4 events in this acceptance window, which converts to a WIMP-nucleon spin-independent cross-section with a minimum of 6.6 × 10-7 pb following the inclusion of an energy-dependent, calibrated, efficiency. A second run is currently underway in which the radon progeny will be eliminated, thereby removing the background population, with a projected sensitivity of 2 × 10-7 pb for similar exposures as the first run.